1. Field of the Invention
The present invention relates to an approximation computation apparatus for calculating an approximate value to an analytical value with a predetermined tolerance maintained and a processing method therefor, and more specifically to such an apparatus and a method for calculating an approximate value to an analytical value of consecutively received time serial data.
2. Description of the Background Art
The wavelet analysis has, in recent years, attracted attention as a frequency analysis in consideration of a time domain among the procedures for finding various features from time serial data. This procedure has been applied to many fields such as compression of image and audio data, image processing on medical images, searching for feature-approximating data of audio or music, and analysis and prediction of earthquake shaking with seismic wave data.
Generally, the wavelet transform computation deals with static time serial data. Although time serial data are called static, such data are consecutively supplied in time serial, thus rendering the real-time wavelet transform computation difficult.
Therefore, some procedures were proposed which approximate wavelet coefficients for the wavelet transform to process consecutively-arriving data with the coefficients, thereby reducing the amount of computation.
A first proposal is described in Anna C. Gilbert, et al., “Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries”, Proceedings of the 27th VLDB Conference, 2001, pp. 79-88. A second proposal is described in Tatsuya Watanabe, et al., “Dimensionality Reduction by Random Projection”, Technical Report of the Institute of Electronics, Information and Communication Engineers, COMP2001-92, 2002, Vol. 101, No. 707, pp. 73-79. A third proposal is described in Dimitris Achlioptas, “Database-Friendly Random Projections”, Proceedings PODS, 2001, pp. 13-22.
These proposals are based on the procedure of calculating, in a data domain reduced by using dimensionality reduction called random projection, wavelet coefficients with a certain tolerance, or acceptable range of error, ensured.
However, in the solutions described in the three documents indicated above, whenever data more than a threshold value n arrive or are received, the computation will result in being erroneous so as to exceed a predetermined tolerance, the threshold value n corresponding to the maximum length of data sequence for calculating an approximate value, i.e. wavelet coefficient, to an analytical value with the predetermined tolerance maintained. Thus, those solutions involve a difficulty that a reception of data more than the threshold value gives rise to failure in assuring a tolerable calculation result. Note that the maximum length of a data sequence is also referred to as the maximum number of data guaranteeing the approximation accuracy.